Distributions of Minimum Bias Current measurements in TileCal

The purpose of this note is to evaluate the spread of Minimum Bias (MB) currents in TileCal, when measured using the existing electronics. This information allows to estimate how many measurements in each cell are needed to obtain a statistical error of 1% of the mean, which is the goal of the MB monitoring system; in turn, this information will be used to design the MB data acquisition system. A reliable estimate of the spread requires the use of signals from several billion bunch crossings, which is way in excess of the available sample of simulated MB collisions. Therefore the simulated MB signals in the TileCal readout cells are parametrized and the analytical forms are used to generate samples of MB signals as large as needed. It is shown that at design luminosity even in the cells with the smallest currents a few tens of measurements should achieve the goal of a 1% error in monitoring the MB current.